Respuesta :
Answer:
There are 56 outcomes are possible if the customer chooses three different vegetables.
Step-by-step explanation:
Given that the vegetables are peppers ,carrots, radishes ,broccoli, fiddle heads, cauliflower, okra and corn.
There are 8 different vegetables in the given group.
A restaurant lunch special allows the customer to choose 3 vegetables from the given group.
To find how many outcomes are possible if the customer chooses three different vegetables :
From the given data the customer has to choose 3 different vegetables from the group.
So, total number of possibilities of selecting 3 vegetables can be solved by Combinations ([tex]^nC_r[/tex])
Here n=8 and r=3
The formula is [tex]^nC_r=\frac{n!}{(n-r)!r!}[/tex]
Substitute the values in the formula we get
[tex]^8C_3=\frac{8!}{(8-3)!3!}[/tex]
We know [tex]n!=n(n-1)(n-2)...3.2.1[/tex]
[tex]^8C_3=\frac{8\times 7\times 6\times 5\times 4\times 3\times 2\times 1}{(5)!3!}[/tex]
[tex]^8C_3=\frac{8\times 7\times 6\times 5\times 4\times 3\times 2\times 1}{5\times 4\times 3\times 2\times 1(3\times 2\times 1)}[/tex]
[tex]=\frac{56}{1}[/tex]
[tex]=56[/tex]
∴ [tex]^8C_3=56[/tex]
